2-functor


In mathematics, a 2-functor is a morphism between 2-categories. They may be defined formally using enrichment by saying that a 2-category is exactly a Cat-enriched category and a 2-functor is a Cat-functor.
Explicitly, if C and D are 2-categories then a 2-functor consists of
such that each strictly preserves identity objects and they commute with horizontal composition in C and D.
See for more details and for lax versions.